With any drug you have an effective range, and a half life. So you need to get a bunch of drug into the system to get into the effective range, then you just need to top-up. So if you had 4 tablets of painkiller that a normal dose was 2 tablets, you might get better relief from taking three off the top, and the other one at the normal dose interval. Also I'm not a doctor. But just for arguments sake, My EDC first aid kit usually has 10-20 painkiller tablets, usually ibuprofen 200mg. thats enough to get me through a few days if needed. I don't understand having only a few tablets unless they are a 24 hour drug. If you need it, you need enough to get you through a period of time.
Now different drugs do different things, so finding which one does what you need it to do is important. your chronic/long acting drugs are great for stuff like normal pain, or allergies, but not as good for the acute stuff. Unfortunately most of the drugs I prefer are unavailable in Oz so I'm learning new ones, and figuring out how they work. Ibuprofen and acetaminophen are the same, so thats easy.
I've even had injuries which required me to stack them in alternating doses, but one has to be careful with that, as you hit the dose limits pretty fast. But for me it was worth being able to sleep for a few hours at a time.
I've seen some first aid kits with all manner of goodies in them, but knowing how you will react is important. Codeine is not great for me, makes my brain fluffy and blocks up my guts. (although that can have its uses too) I wouldn't want to take it in a solo situation, but if someone else was there to do the thinking, I'd be okay with it if needed.
Splinting and wrapping also helps, but I'm of the general opinion that if you need to wrap it, you should stay off it, but in an emergency, it could give you that edge.
Again, I'm no doctor, just have a few nurses in my immediate family, and some emergency/sport med training. But there is a lot of bad info around when it comes to soft-tissue type injuries, even among those who should know better. So my info may be wrong, as I only have a test sample of 1, but for me it works.